login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202502 Modified lower triangular Fibonacci matrix, by antidiagonals. 2
1, 0, 2, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 3, 8, 0, 0, 0, 2, 5, 13, 0, 0, 0, 1, 3, 8, 21, 0, 0, 0, 0, 2, 5, 13, 34, 0, 0, 0, 0, 1, 3, 8, 21, 55, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55, 144, 0, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 233, 0, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This matrix, P, is used to form the Fibonacci self-fission matrix as the product P*Q, where Q is the upper triangular Fibonacci matrix, A202451.  To form P, delete the main diagonal of the transpose of Q.

LINKS

Table of n, a(n) for n=1..89.

Clark Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195-202.

EXAMPLE

Northwest corner:

1...0...0...0...0...0...0...0...0

2...1...0...0...0...0...0...0...0

3...2...1...0...0...0...0...0...0

5...3...2...1...1...0...0...0...0

8...5...3...2...1...1...0...0...0

MATHEMATICA

n = 14;

Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[Fibonacci[k], {k, 1, n}]];

Qt = Transpose[Q]; P1 = Qt - IdentityMatrix[n];

P = P1[[Range[2, n], Range[1, n]]];

F = P.Q;

Flatten[Table[P[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202502 as a sequence *)

Flatten[Table[Q[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202451 as a sequence *)

Flatten[Table[F[[i]][[k + 1 - i]], {k, 1, n - 1}, {i, 1, k}]] (* A202503 as a sequence *)

TableForm[P]  (* A202502, modified lower triangular Fibonacci matrix *)

TableForm[Q] (* A202451, upper tri. Fibonacci matrix *)

TableForm[F] (* A202503, Fibonacci self-fission matrix *)

CROSSREFS

Cf. A202503, A202451, A202452, A202453, A000045.

Sequence in context: A062283 A136493 A132213 * A219839 A154312 A236076

Adjacent sequences:  A202499 A202500 A202501 * A202503 A202504 A202505

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 20 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 31 17:36 EDT 2020. Contains 333151 sequences. (Running on oeis4.)